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Mexico National Olympiad
2013 Mexico National Olympiad
3
3
Part of
2013 Mexico National Olympiad
Problems
(1)
Largest Subset
Source: Mexican Mathematical Olympiad 2013 Problem 3
12/1/2013
What is the largest amount of elements that can be taken from the set
{
1
,
2
,
.
.
.
,
2012
,
2013
}
\{1, 2, ... , 2012, 2013\}
{
1
,
2
,
...
,
2012
,
2013
}
, such that within them there are no distinct three, say
a
a
a
,
b
b
b
,and
c
c
c
, such that
a
a
a
is a divisor or multiple of
b
ā
c
b-c
b
ā
c
?
combinatorics proposed
combinatorics